TESTING INTERNATIONAL PRICE TRANSMISSION UNDER ...

Empirical Tests for Spatial Price Analysis
3.3.1 Unit root tests applied to price series
Understanding the time series properties of the data is a prerequisite for any
cointegration analysis which, as explained in the previous paragraph, normally
requires the time series to be I(1).
Empirical tests, motivated by a vast literature on unit roots and error correction
models, often find evidence of unit roots in commodity prices, though according
to price theory price series need not have unit roots. Indeed, price theory states
that commodity prices will be auto correlated convergent series, which arises from
the biological nature of commodity production and the storage and arbitrage costs
over time (Wang and Tomek 2007, p.873).
Moreover, the outcome of unit root tests is likely to be affected by a number of
factors, first of all alternate test specifications (Wang and Tomek 2007, p.875).
Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests have low
power against the alternative that the series is stationary; for this reason,
Kwiatkowski, Phillips, Schmidt e Shin (KPPS) tests, having the null hypothesis of
stationarity, can be used as a consistency check, though, often, neither test will
reject (Tomek and Myers 1993, p.189). Wang and Tomek (2007) find that unit
root tests results are sensitive to the test equation specification, and that evidence
favouring unit roots in commodity prices is not strong. Data transformations
(using the series in nominal or in real terms, or in logs) should strictly depend
upon the research questions which are asked. Data frequency also plays a role 32 .
Finally, if the number of lags used for the unit root tests is too small, then the
inference about the existence of a unit root is biased; if is too large, the finite
sample properties of unit root tests are likely to deteriorate, and an inefficient
estimate is obtained.
Structural breaks also represent an important object of analysis. It is well
known that failure to allow for an existing structural break while testing for unit
roots leads to a bias that reduces the ability to reject a (false) unit root null
hypothesis. If a structural break has occurred, but is not modelled in the test
equation, then standard ADF tests will be biased towards non-rejection of the null
hypothesis. For this reason, Perron and Vogelsang (1992) have extended the ADF
specification to allow for possible structural breaks in the time series. They
propose two tests which allow for the existence of one endogenous structural
break both under the null hypothesis of non-stationarity and under the alternative
hypothesis of stationarity. The Additive Outlier (AO) test, by using a dummy
32 Defining the total number of observations as T, which is given by the product between span of the sample S
and the frequency f , the consistency and the power of the tests as f increases depend upon the assumptions on
S. If S is fixed, as f increases the power of tests increases but ultimately levels off. If the assumption of a
fixed S is relaxed, it appears that the frequency of the sample is more important than the number of
observations in determining the power of the test, but this of course assumes a constant structure of the data
generating process, which might not be the case as S increases (Wang and Tomek 2007, p.877).
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